2010/09/03 by Xing Sun, Andrew B. Nobel, Sun, Xing +1 · 2 citations
Computer Science · Mathematics · #60B20 #60C05 #Bayesian Methods and Mixture Models #Block (permutation group theory) #Block matrix #Block size #Combinatorics #Computer science #Constant (computer programming) #Data Management and Algorithms #FOS: Mathematics #Gaussian #Mathematics #Matrix (chemical analysis) #Physics #Probability (math.PR) #Random Matrices and Applications #Statistics #Statistics Theory (math.ST) #math.PR #math.ST #msc:60B20 #msc:60C05 #stat.TH
paper · pdf · doi:10.48550/arxiv.1009.0562
published in arXiv (Cornell University) (Cornell University) · 25 pages, 3 figures
arxiv created 2010/09/03 · openalex publication_date 2010/09/03 · arxiv updated 2010/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We investigate the maximal size of distinguished submatrices of a Gaussian random matrix. Of interest are submatrices whose entries have average greater than or equal to a positive constant, and submatrices whose entries are well-fit by a two-way ANOVA model. We identify size thresholds and associated (asymptotic) probability bounds for both large-average and ANOVA-fit submatrices. Results are obtained when the matrix and submatrices of interest are square, and in rectangular cases when the matrix submatrices of interest have fixed aspect ratios. In addition, we obtain a strong, interval concentration result for the size of large average submatrices in the square case. A simulation study shows good agreement between the observed and predicted sizes of large average submatrices in matrices of moderate size.